Decorrelation-Based Feature Discovery: Activity-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data Source https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6960825/

Mohino-Herranz I, Gil-Pita R, Rosa-Zurera M, Seoane F. Activity Recognition Using Wearable Physiological Measurements: Selection of Features from a Comprehensive Literature Study. Sensors (Basel). 2019 Dec 13;19(24):0. doi: 10.3390/s19245524. PMID: 31847261; PMCID: PMC6960825.

1.2 The Data

Activitydata <- read.csv("~/GitHub/LatentBiomarkers/Data/ActivityData/data.txt", header=FALSE, stringsAsFactors=TRUE)
featNames <- read.table("~/GitHub/LatentBiomarkers/Data/ActivityData/Featurelabels.txt", quote="\"", comment.char="")
featNames <- as.character(t(featNames))
featNames <- str_replace_all(featNames,"\\(abs\\)","_A_")
featNames[duplicated(featNames)] <- paste(featNames[duplicated(featNames)],"D",sep="_")

rep_ID <- numeric(nrow(Activitydata))
ctr <- 1
for (ind in c(1:(nrow(Activitydata)-1)))
{
  rep_ID[ind] <- ctr
  if (Activitydata$V1[ind] != Activitydata$V1[ind+1]) ctr <- 0;
  ctr <- ctr + 1
}
rownames(Activitydata) <- paste(Activitydata$V1,rep_ID,sep="_")
colnames(Activitydata) <- c("ID",featNames,"class")
Activitydata$rep <- rep_ID
  
tb <- table(Activitydata$class)

classes <- c("Neu","Emo","Men","Phy")
names(classes) <- names(tb)
Activitydata$class <- classes[as.character(Activitydata$class)]
table(Activitydata$class)
#> 
#>  Emo  Men  Neu  Phy 
#> 1120 1120 1120 1120



ID_class <- paste(Activitydata$ID,Activitydata$class)
IDCLASS <- unique(ID_class)
theclass <- Activitydata$class[!duplicated(ID_class)]
theIDs <- Activitydata$ID[!duplicated(ID_class)]

ActivitydataAvg <- NULL
for (id in IDCLASS)
{
  ActivitydataAvg <- rbind(ActivitydataAvg,apply(Activitydata[ID_class==id,featNames],2,mean))
}
colnames(ActivitydataAvg) <- featNames
rownames(ActivitydataAvg) <- IDCLASS
ActivitydataAvg <- as.data.frame(ActivitydataAvg)
ActivitydataAvg$class <- theclass
ActivitydataAvg$ID <- theIDs

table(ActivitydataAvg$class)
#> 
#> Emo Men Neu Phy 
#>  40  40  40  40


ActivitydataAvg <- subset(ActivitydataAvg, class=="Men" | class=="Emo")

ActivitydataAvg$class <- 1*(ActivitydataAvg$class == "Men")
table(ActivitydataAvg$class)
#> 
#>  0  1 
#> 40 40

1.2.0.1 Standarize the names for the reporting

studyName <- "Activity"
dataframe <- ActivitydataAvg
outcome <- "class"

TopVariables <- 10
thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
80	534

pander::pander(table(dataframe[,outcome]))

0	1
40	40

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1000

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]


dataframe <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

if (!largeSet)
{
  
  hm <- heatMaps(data=dataframe,
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 1

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 362 , Uni p: 0.01628202 , Uncorrelated Base: 62 , Outcome-Driven Size: 0 , Base Size: 62 
#> 
#> 
 1 <R=1.000,w=  1,N=  265>, Top: 47( 21 )[ 1 : 47 Fa= 47 : 0.975 ]( 47 , 183 , 0 ),<|>Tot Used: 230 , Added: 183 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=1.000,w=  1,N=  265>, Top: 28( 6 )[ 1 : 28 Fa= 74 : 0.975 ]( 27 , 94 , 47 ),<|>Tot Used: 258 , Added: 94 , Zero Std: 0 , Max Cor: 1.000
#> 
 3 <R=1.000,w=  1,N=  265>, Top: 10( 2 )[ 1 : 10 Fa= 84 : 0.975 ]( 10 , 20 , 74 ),<|>Tot Used: 258 , Added: 20 , Zero Std: 0 , Max Cor: 1.000
#> 
 4 <R=1.000,w=  2,N=   92>, Top: 37( 1 )[ 1 : 37 Fa= 99 : 0.950 ]( 37 , 45 , 84 ),<|>Tot Used: 280 , Added: 45 , Zero Std: 0 , Max Cor: 0.992
#> 
 5 <R=0.992,w=  2,N=   92>, Top: 10( 1 )[ 1 : 10 Fa= 100 : 0.946 ]( 10 , 10 , 99 ),<|>Tot Used: 280 , Added: 10 , Zero Std: 0 , Max Cor: 0.946
#> 
 6 <R=0.946,w=  2,N=   92>, Top: 19( 1 )[ 1 : 19 Fa= 107 : 0.923 ]( 19 , 20 , 100 ),<|>Tot Used: 289 , Added: 20 , Zero Std: 0 , Max Cor: 0.983
#> 
 7 <R=0.983,w=  2,N=   92>, Top: 1( 1 )[ 1 : 1 Fa= 107 : 0.941 ]( 1 , 1 , 107 ),<|>Tot Used: 289 , Added: 1 , Zero Std: 0 , Max Cor: 0.930
#> 
 8 <R=0.930,w=  3,N=   85>, Top: 31( 2 )[ 1 : 31 Fa= 118 : 0.865 ]( 31 , 38 , 107 ),<|>Tot Used: 303 , Added: 38 , Zero Std: 0 , Max Cor: 0.983
#> 
 9 <R=0.983,w=  3,N=   85>, Top: 10( 1 )[ 1 : 10 Fa= 119 : 0.892 ]( 8 , 10 , 118 ),<|>Tot Used: 307 , Added: 10 , Zero Std: 0 , Max Cor: 0.954
#> 
 10 <R=0.954,w=  3,N=   85>, Top: 2( 1 )[ 1 : 2 Fa= 121 : 0.877 ]( 2 , 2 , 119 ),<|>Tot Used: 307 , Added: 2 , Zero Std: 0 , Max Cor: 0.963
#> 
 11 <R=0.963,w=  4,N=   62>, Top: 29( 2 )[ 1 : 29 Fa= 131 : 0.832 ]( 27 , 30 , 121 ),<|>Tot Used: 312 , Added: 30 , Zero Std: 0 , Max Cor: 0.891
#> 
 12 <R=0.891,w=  4,N=   62>, Top: 25( 1 )[ 1 : 25 Fa= 136 : 0.800 ]( 24 , 27 , 131 ),<|>Tot Used: 317 , Added: 27 , Zero Std: 0 , Max Cor: 0.988
#> 
 13 <R=0.988,w=  4,N=   62>, Top: 2( 1 )[ 1 : 2 Fa= 138 : 0.844 ]( 2 , 2 , 136 ),<|>Tot Used: 317 , Added: 2 , Zero Std: 0 , Max Cor: 0.981
#> 
 14 <R=0.981,w=  5,N=    6>, Top: 3( 1 )[ 1 : 3 Fa= 139 : 0.800 ]( 3 , 3 , 138 ),<|>Tot Used: 317 , Added: 3 , Zero Std: 0 , Max Cor: 0.804
#> 
 15 <R=0.804,w=  5,N=    6>, Top: 1( 1 )[ 1 : 1 Fa= 140 : 0.800 ]( 1 , 1 , 139 ),<|>Tot Used: 317 , Added: 1 , Zero Std: 0 , Max Cor: 0.798
#> 
 16 <R=0.798,w=  6,N=    0>
#> 
 [ 16 ], 0.7983933 Decor Dimension: 317 . Cor to Base: 195 , ABase: 31 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

616

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

158

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.84

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

3.12

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe,
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9976649

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data

classes <- unique(dataframe[,outcome])
raincolors <- rainbow(length(classes))
names(raincolors) <- classes
datasetframe.umap = umap(scale(dataframe[,varlist]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
text(datasetframe.umap$layout,labels=dataframe[,outcome],col=raincolors[dataframe[,outcome]+1])

1.8.2 The decorralted UMAP

datasetframe.umap = umap(scale(DEdataframe[,varlistc]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
text(datasetframe.umap$layout,labels=DEdataframe[,outcome],col=raincolors[DEdataframe[,outcome]+1])

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : ECG_p_LF_mean 200 : IT_CCV_LF 300 : EDA_Original_mad_D

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_ECG_p_LF_mean 200 : La_IT_CCV_LF 300 : La_EDA_Original_mad_D

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##topfive
topvar <- c(1:length(varlist)) <= TopVariables
pander::pander(univarRAW$orderframe[topvar,univariate_columns])

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
ECG_hrv_prctile75	0.483	1.031	-0.1471	1.286	0.0849	0.731
ECG_hrv_geomean_A_	-0.105	1.208	0.5327	1.093	0.1001	0.727
IT_LF_baseline_D	0.518	1.044	-0.2219	0.700	0.5845	0.721
IT_p_Total_baseline	0.507	1.009	-0.2168	0.668	0.6797	0.721
IT_VLF_baseline	0.492	0.990	-0.2217	0.652	0.7285	0.720
ECG_hrv_prctile25	0.244	1.150	-0.4451	0.938	0.5416	0.719
IT_PSD_baseline	0.554	1.095	-0.1829	0.773	0.2875	0.715
ECG_hrv_mean	0.259	0.865	-0.3517	0.931	0.2559	0.714
IT_HF_baseline	0.692	1.254	-0.0466	1.052	0.0555	0.713
ECG_hrv_trimmean25	0.282	0.950	-0.3372	0.967	0.5083	0.711

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]

theLaVar <- rownames(finalTable)[str_detect(rownames(finalTable),"La_")]

pander::pander(univarDe$orderframe[topLAvar,univariate_columns])

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
La_IT_BRV_baseline	-0.15629	0.4237	0.1964	0.2851	0.9649	0.759
**La_EDA_processed_geomean_A__D**	0.29051	0.5653	-0.2026	0.4549	0.7895	0.742
La_EDA_Filt1_mad_D	-0.01455	0.0533	0.0233	0.0324	0.3238	0.733
La_ECG_HR_min_div_baseline	0.06680	0.4682	0.2872	0.4039	0.0950	0.731
La_ECG_RR_window_baseline	0.14303	0.2844	-0.0680	0.2889	0.9594	0.729
La_EDA_processed_std_D	0.24649	0.3816	-0.0880	0.3304	0.1748	0.724
IT_p_Total_baseline	0.50669	1.0086	-0.2168	0.6684	0.6797	0.721
La_EDA_Original_max_D	0.00529	0.0520	-0.0230	0.0302	0.0128	0.716
ECG_hrv_mean	0.25862	0.8655	-0.3517	0.9306	0.2559	0.714
La_EDA_processed_trimmean25_D	0.21468	0.6566	-0.1355	0.3130	0.4613	0.710

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")

theSigDc <- dc[theLaVar]
names(theSigDc) <- NULL
theSigDc <- unique(names(unlist(theSigDc)))


theFormulas <- dc[rownames(finalTable)]
deFromula <- character(length(theFormulas))
names(deFromula) <- rownames(finalTable)

pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.85	281	0.77

allSigvars <- names(dc)



dx <- names(deFromula)[1]
for (dx in names(deFromula))
{
  coef <- theFormulas[[dx]]
  cname <- names(theFormulas[[dx]])
  names(cname) <- cname
  for (cf in names(coef))
  {
    if (cf != dx)
    {
      if (coef[cf]>0)
      {
        deFromula[dx] <- paste(deFromula[dx],
                               sprintf("+ %5.3f*%s",coef[cf],cname[cf]))
      }
      else
      {
        deFromula[dx] <- paste(deFromula[dx],
                               sprintf("%5.3f*%s",coef[cf],cname[cf]))
      }
    }
  }
}

finalTable <- rbind(finalTable,univarRAW$orderframe[theSigDc[!(theSigDc %in% rownames(finalTable))],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- deFromula[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
La_IT_BRV_baseline	-0.832IT_BRV_prctile25 + 1.000IT_BRV_baseline	-0.15629	0.4237	0.19644	0.2851	0.96495	0.759	0.642	-1
**La_EDA_processed_geomean_A__D**	+ 1.000*EDA_processed_geomean_A__D -0.977*EDA_Filt2_std_D	0.29051	0.5653	-0.20256	0.4549	0.78945	0.742	0.601	2
La_EDA_Filt1_mad_D	+ 1.000EDA_Filt1_mad_D -1.026EDA_Filt2_std_D	-0.01455	0.0533	0.02326	0.0324	0.32376	0.733	0.508	0
La_ECG_HR_min_div_baseline	+ 0.912ECG_RR_window_geomean_A_ + 1.000ECG_HR_min_div_baseline	0.06680	0.4682	0.28718	0.4039	0.09500	0.731	0.518	-1
La_ECG_RR_window_baseline	-0.914ECG_RR_window_geomean_A_ + 1.000ECG_RR_window_baseline	0.14303	0.2844	-0.06795	0.2889	0.95939	0.729	0.522	-1
La_EDA_processed_std_D	+ 1.000EDA_processed_std_D -0.890EDA_Filt2_std_D	0.24649	0.3816	-0.08800	0.3304	0.17475	0.724	0.581	1
IT_p_Total_baseline		0.50669	1.0086	-0.21676	0.6684	0.67972	0.721	0.721	5
La_EDA_Original_max_D	+ 1.000EDA_Original_max_D -1.797EDA_Original_prctile75_D + 0.805*EDA_Filt1_prctile25_D	0.00529	0.0520	-0.02299	0.0302	0.01285	0.716	0.575	-2
ECG_hrv_mean		0.25862	0.8655	-0.35169	0.9306	0.25586	0.714	0.714	4
La_EDA_processed_trimmean25_D	+ 1.000EDA_processed_trimmean25_D -0.932EDA_processed_median_D	0.21468	0.6566	-0.13552	0.3130	0.46134	0.710	0.582	-1
IT_BRV_baseline	NA	-0.35971	0.8468	-0.00106	1.0856	0.08274	0.642	0.642	NA
ECG_RR_window_geomean_A_	NA	-0.09206	0.9615	0.20263	0.9615	0.99561	0.603	0.603	15
**EDA_processed_geomean_A__D**	NA	0.68903	1.3691	0.21447	1.0251	0.05106	0.601	0.601	NA
EDA_processed_trimmean25_D	NA	-0.39525	1.3811	-0.61752	1.3648	0.01157	0.582	0.582	NA
EDA_processed_std_D	NA	0.60948	1.1881	0.29184	0.9118	0.01488	0.581	0.581	NA
EDA_Original_max_D	NA	0.63696	1.3434	0.36718	1.1892	0.00726	0.575	0.575	NA
EDA_Filt1_prctile25_D	NA	0.66089	1.4082	0.37552	1.2296	0.00966	0.573	0.573	34
EDA_Original_prctile75_D	NA	0.64742	1.3754	0.38526	1.2143	0.01041	0.570	0.570	NA
EDA_processed_median_D	NA	-0.65445	1.3990	-0.51718	1.3120	0.00378	0.530	0.530	NA
ECG_RR_window_baseline	NA	0.05886	0.9529	0.11732	0.9276	0.77168	0.522	0.522	NA
ECG_HR_min_div_baseline	NA	0.15072	1.0047	0.10247	0.9849	0.67448	0.518	0.518	NA
EDA_Filt1_mad_D	NA	0.40391	1.0951	0.46113	1.1993	0.01682	0.508	0.508	NA
IT_BRV_prctile25	NA	-0.24439	1.0856	-0.23727	1.0882	0.27464	0.503	0.503	5
EDA_Filt2_std_D	NA	0.40783	1.0812	0.42676	1.1548	0.02041	0.489	0.489	11